A Study of Unsteady Natural Convection in Cryogenic Storage Tanks for Densified Propellants

A two-dimensional, unsteady, two domain (liquid and vapor) mathematical model is adopted to investigate the thermo-hydrodynamic behavior of a propellant in a cryogenic storage tank. The physics based mathematical model consists of conservation of mass, momentum, and energy equations for the liquid subjected to variable boundary conditions at the liquidvapor interface and constant heat flux boundary condition at the walls of the container. The density of the liquid is assumed to be temperature dependent only in the buoyancy term of the momentum equation (Boussinesq approximation). The vapor in the ullage is assumed to be an ideal gas with uniform thermodynamic properties and is modeled by single node conservation equations for mass and energy. The two domains are coupled through a set of interface equations for mass and energy exchange between the liquid and the vapor. The resulting nonlinear governing equations for the liquid domain are solved by an implicit finite difference technique (where the pressure distribution is determined by solving the Poisson’s equation) to predict the transient temperature and velocity fields inside the propellant. The equations for the vapor are solved by a simple explicit finite difference technique. The model is tested for a benchmark case (numerically and experimentally) to verify the accuracy of the numerical scheme. Finally, the model is used to predict the transient circulation patterns and resulting thermal stratification in a densified cryogenic propellant for a constant wall heat flux boundary condition.